What is the fundamental reason for the difference between yellow-orange and red-orange?

Correct answer: A different primary colour mixed with orange

The governing concept is tertiary-colour formation on the colour wheel. Yellow-orange is produced by combining yellow with orange, whereas red-orange is produced by combining red with orange. Therefore, the different primary component changes the colour bias and explains the difference. Paper surface and brush size do not define the hue, while white would mainly change lightness or tint rather than create this named relationship.